On numerical investigation of the nonmodal instability of the Poiseuille flow in an elliptic pipe

For the Poiseuille flow in a pipe of axially uniform elliptic cross-section the dependence of the maximum amplification of the average kinetic energy density of disturbances on the pipe aspect ratio is computed. It is shown, that for the considered values of streamwise wavenumber and the Reynolds number the maximum amplification decreases non-monotonically as the pipe aspect ratio increases under scaling providing the same flow rates at the same Reynolds numbers. It is also shown, that the optimal disturbances displaying the maximum energy growth are streamwise vortices.